Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2001-012 (November 15, 2001)
A New Relaxation Method for Mathematical Programs with Complementarity Constraints
by Gui-Hua Lin and Masao Fukushima
In this paper, we present a new relaxation method for mathematical
programs with complementarity constraints. Based on the fact that a variational
inequality problem defined on a simplex can be represented by a finite number of
inequalities, we use an expansive simplex instead of the nonnegative orthant involved
in the complementarity constraints. We then remove some inequalities and obtain a
standard nonlinear program. Constraint qualification or the Mangasarian-Fromovitz
constraint qualification holds for the relaxed problem under some mild conditions.
We also consider a limiting behavior of the relaxed problem. In particular, we show
that any accumulation point of stationary points of the relaxed problems is a weakly
stationary point of the original problem and if the function involved in the
complementarity constraints does not vanish at this point, it is C-stationary.
Furthermore, under some suitable conditions, it is B-stationary.